Practical Geometry Tasks as a Method for Teaching Active Learning in Geometry

A lot of research has indicated that the way students are taught has a strong influence and impact on their ideas about the subject and how the subject should be taught. In 1908 at the International Congress of Mathematicians in Rome the great mathematician Felix Klein (1849 - 1925) talked about the paradox of double forgetting. The essence of the paradox is the life experience of young teachers who have to forget about a lot of university training and its scientific thinking to successfully teach mathematics. This phenomenon currently persists at Slovak primary and secondary schools. The problem is especially striking in teaching geometry. Many Slovak and Czech teachers agree that geometry has many applications in everyday life, but there is not enough "real-life" everyday problems in Slovak mathematics textbooks which are structured according to the deductive approach to teaching and learning. Based on the concept of realistic mathematics education, we deal with the implementation of special geometrical tasks called topographical tasks in teacher training. Our findings are based on real experiences teaching through workshops devoted to topographical tasks which were realized during two school lessons. In the conclusion we analysed the benefits of this new approach to active teaching. The students' solutions to the tasks and their methodological analysis are included, too. (C) 2015 The Authors. Published by Elsevier Ltd.